Numerical simulations of boundary layer transition by combined compact difference methods - Chen, Weijia. (2013)
The objective of this study is to produce a stable and accurate numerical model for investigating the physical mechanism of boundary layer transition. A velocity–vorticity formulation of the unsteady, incompressible Navier–Stokes (NS) equations is used to simulate the boundary layer transition process under excitation by small-amplitude time-dependent disturbances. To capture the non-linear wave dynamics in the transition process, Combined Compact Difference (CCD) schemes up to 12th order accuracy are constructed. On a uniform grid, for the streamwise direction, an upwind CCD scheme is co-optimized with a 5-6 alternating-stage Runge–Kutta temporal scheme. In this method, the dispersion and dissipation errors are optimized to simulate physical waves accurately. Simultaneously, the schemes can efficiently suppress numerical grid-mesh oscillations. On a non-uniform grid, for the wall-normal direction, CCD schemes are derived based on generalized polynomial interpolation. A new 2-piecewise function is also provided for the generation of non-uniform grid. Excellent stability properties and spectral resolution are observed when CCD schemes are implemented with this grid-generation method. The numerical methods for simulating the transition simulation have been validated with theoretical, experimental, and other simulation results. The present numerical model is used to investigate the vortex dynamics in the boundary layer transition under excitation by random disturbances. Although coherent structures are found in random spatial locations and have distorted shapes compared to those in the typical transition process, their localized properties are quite universal. Further, a Soliton-like Coherent Structure (SCS) is shown to play a dominant role in the vortex evolution process. The present simulation results support recent published finding that a universal scenario may underlie the boundary layer transition.